Error Analysis
Error Case Analysis
School of Education, Liberty University
EDLC 530: Teaching Mathematics
Error Analysis
Case Study Level A, Case 1 – Dalton
Dalton is a seventh-grade student with strong foundational mathematics skills that has
been struggling in multiplying decimals.
Student Errors
In Case study level A Case 1, Dalton’s work has decimal errors as he is placing the
decimal in the appropriate place of the product when multiplying and dividing. It appears to be
a procedural error as he may need further understanding of place values when relating to
multiplying and dividing decimals. (2016 pp. 8) From the answers that Dalton provided, it shows
that he is correctly multiplying the numerals but is not applying proper decimal rules when
moving through the product. For example, in number one, he uses two decimal place values in
the product as .78 goes up to the hundredths place value and 9.6 uses only the tenth-place
value. He uses the hundredths place value in his product to end up with the answer 74.88
instead of moving the decimal a combined three place values to end up with 7.488. This is
evident throughout all of his answers even with problem eleven where he ends up with the right
answer, but due to it using money by a whole number, the place values are already lined up
properly.
Strategies
Due to constant procedural errors and Dalton having strong foundational mathematics
skills, we can interview the student and ask him how he determined the outcome of the decimal
placement and notice if he continues the pattern. After interviewing with the student, the
teacher can try to discuss the error and attempt to tell Dalton how to properly use the place
values when multiplying decimals. Since Dalton already possesses strong foundational skills, the
teacher can do a review on decimal placement when multiplying and conduct the scaffolding
method where the teacher builds off the skills that Dalton has and chunk the problems into
smaller more manageable problems to further his understanding. (2016 pp. 20) This will serve in
playing on his foundational strengths that he already possesses in mathematics and help him
further his understanding of the concept. The teacher can provide prompts and ask specific
questions that relates to his decimal misunderstandings. These will help Dalton improve as he
has a misconception of the decimal values and may need a better understanding and the
teacher can point out any misunderstandings that he may have.
Case Study Level A, Case 2 – Madison
Madison is a second-grade student with a specific learning disability in math who had
just exceled in a lesson on money through the use of manipulatives. In her IEP it states that she
learns better through the use of concrete objects in learning. She is now struggling with the
concept of time, specifically the term quarter.
Student Errors
In case study level A, Case 2, Madison’s work appears to be correct when matching
numerical and simple words to the appropriate time such as 8:10 or half past ten and seven
thirty. The confusion lies with the terms quarter past or quarter ‘til where she interprets it as 25
which can be carried understanding from the previous math lesson where a quarter equals 25
cents. From the answers that Madison provided, she seems to have a factual error of not
knowing proper mathematical terms of “quarter” when relating to time. (2016 pp. 6) For
example, in problems six and ten, it reads “quarter past” and Madison puts the big hand on the
five, which equals 25 in minutes. For problem eight, it reads a “quarter ‘til four” and she puts
the big hand on the seven which shows 25 more minutes until she gets to four. This is all evident
Error Analysis
of an overgeneralizing conceptual error due to her incorrectly applying her previous knowledge
and rules that she had from previous situations such as money and applying it wrongly with
time.
Strategies
The teacher can implement a reassessment of the skill using her previous knowledge of
clocks while focusing on quarter or quarter ‘til problems since that’s where she struggles. Using
this the teacher can explain the meaning of these terms so that she can properly connect it with
time as she has previous knowledge and ideas so there’s no need to reteach the whole lesson.
When the vocabulary is retaught, the teacher can use guided practice where Madison can
complete quarter problems relative to clocks with the help of teacher or her peers. Through this
the teacher can monitor her work closely and give positive or corrective feedback depending on
the answers given. (2016 pp. 20) Due to her IEP stating that she understands with more
concrete objects, the teacher can visually show her a quarter of a circle and then measure it to
the clock to show that from twelve to three measures a quarter on the clock, which is also
fifteen minutes. The manipulatives will help Madison’s learning through the use of concrete
examples stated in her IEP which will allow her to better learn the material. With the guided
practice, the teacher can play close attention and correct Madison’s errors in real time and
properly praise her correct answers which will help her see when the work is being done
correctly.
Case Study Level B, Case 2 – Elias
Elias is a second-grade student with a learning disability who has not been making
enough progress to meet his end-of-year goals.
Student Errors
In case study level B, Case 2, Elias’ work has regrouping errors as he is not regrouping
properly when getting the sum. It is evident that he is exhibiting a procedural error and needs
further understanding of how to regroup one group of ten to the tens column. (2016 pp. 7)
From the answers that Elias has provided, it shows that he has conceptual knowledge when
adding and subtracting multi-digit numbers but needs further practice with just regrouping. For
example, in number one he adds eight and two in the one’s place and puts ten in the sum and
then adds two and one in the tens place to get a full sum of 310 instead of regrouping the ten
from the one’s place to get the correct sum of 40. He correctly adds and subtracts the problems
where regrouping is not needed, which shows evidence of his conceptual knowledge and ability
to add and subtract when using place values. Due to this, we can see that he just needs to
further his procedural understanding of regrouping.
Strategies
The teacher can provide specific instruction to discuss why Elias struggles with the
procedure of regrouping and focus on working with him so that he can gain understanding of
regrouping. (2016 pp. 18) An effective strategy that can help Elias is the use of manipulatives
specifically base ten blocks which can be used to properly model and visually model the concept
of regrouping. Manipulatives include objects or items that students can physically use to help
them see representation in the mathematical idea that they are trying to learn when matching
the specific instruction from the teacher. Another strategy that the teacher may implement is
the use of modeling with the manipulatives. (2016 pp. 20) The strategy of modeling and
manipulatives will allow the teacher to visually show Elias how regrouping is a real-life scenario
by adding the numbers in the one column and transferring them over to a base the block when
they exceed ten. Through the use of modeling, the teacher can use sample problems as the
Error Analysis
teacher can guide Elias and point out any misconceptions that he has when it comes to
regrouping. These strategies can help as he will receive clear instructions along with practice
from the teacher or paraprofessional. With his understanding of fundamental math concepts,
he will be able to learn through the use of visual learning and further understanding from his
teacher.
Case Study Level C, Case 1 – Wyatt
Wyatt is a sixth-grade student who has been struggling in multiplying fractions,
specifically those with common denominators. He had previously shown great understanding of
adding and subtracting fractions.
Student Errors
In case study level C, Case 1, Wyatt’s work has fraction errors and fails to change the
denominator when multiplying fractions with common denominators without visual
representation. It appears to be a procedural error as he may not fully understand the rules
when multiplying with common denominators. (2016 pp. 8) From the answers that Wyatt
provided, it shows that he is accurately multiplying the denominators when they are different
but is not applying the same method when the denominators are the same, instead he keeps
the denominator the same in the fraction in the product. For example, in question one, when
given 1/2 times 1/4, he gets the correct answer 1/8, but in question six we can see an error
when he multiplies 2/11 by 6/11, he keeps the denominator the same and ends up with the
answer 12/11 instead of multiplying the denominators of eleven and eleven to get the fraction
12/121 as the final product. This is evident in all of the examples provided with common
denominators.
Strategies
Due to the errors Wyatt has with common denominators with lack of visuals, the teacher
can begin the address the problem he has through guided practice by using his prerequisite
skills. Since he has knowledge of multiplying fractions with different denominators, feedback
can be provided where the teacher can provide constructive criticism towards the student’s
work and provide corrections towards his mistakes. (2016 pp. 20) Through this, the teacher can
inform Wyatt that he must also multiply the denominators when they are similar just as you
would if they were different. An introduction or review of this rule along with practice can help
Wyatt understand and fix his errors. Another strategy that can be utilized is the use of
manipulatives. Manipulatives allow students to use objects so that they can better understand
the content before using an abstract approach. (2016 pp. 19) The teacher can use fraction
blocks or fraction strips so that Wyatt can visually see the answer which can help. After he gains
a better understanding of the denominator rule, the teacher can move away from the concrete
representation towards an abstract when he understands the concepts better. This will help him
use his current knowledge of multiplying fractions to improve on his misunderstanding that he
possesses as he understands the basics of multiplying fractions. When addressing the error of
multiplying with common denominators, the teacher can point out and correct the errors Wyatt
has through feedback and visually show him how to multiply when the denominators are similar
using fraction strips which can help as he correctly answered the question when he was
provided with a circle for visual representation.
